Atomic ratio

The atomic ratio is a measure of the ratio of atoms of one kind (i) to another kind (j). A closely related concept is the atomic percent (or at.%), which gives the percentage of one kind of atom relative to the total number of atoms.^[1] The molecular equivalents of these concepts are the molar fraction, or molar percent.

Atoms

Mathematically, the atomic percent is

{\mathrm {atomic\ percent}}\ ({\mathrm {i}})={\frac {N_{{\mathrm {i}}}}{N_{{\mathrm {tot}}}}}\times 100\

where N_i are the number of atoms of interest and N_tot are the total number of atoms, while the atomic ratio is

{\mathrm {atomic\ ratio}}\ ({\mathrm {i:j}})={\mathrm {atomic\ percent}}\ ({\mathrm {i}}):{\mathrm {atomic\ percent}}\ ({\mathrm {j}})\ .

For example, the atomic percent of hydrogen in water (H₂O) is at.%_H₂O = 2/3 x 100 ≈ 66.67%, while the atomic ratio of hydrogen to oxygen is A_H:O = 2:1.

Isotopes

Another application is in radiochemistry, where this may refer to isotopic ratios or isotopic abundances. Mathematically, the isotopic abundance is

{\mathrm {isotopic\ abundance}}\ ({\mathrm {i}})={\frac {N_{{\mathrm {i}}}}{N_{{\mathrm {tot}}}}}\ ,

where N_i are the number of atoms of the isotope of interest and N_tot is the total number of atoms, while the atomic ratio is

{\mathrm {isotopic\ ratio}}\ ({\mathrm {i:j}})={\mathrm {isotopic\ percent}}\ ({\mathrm {i}}):{\mathrm {isotopic\ percent}}\ ({\mathrm {j}})\ .

For example, the isotopic ratio of deuterium (D) to hydrogen (H) in heavy water is roughly D:H = 1:7000 (corresponding to an isotopic abundance of 0.00014%).

Doping in laser physics

In laser physics however, the atomic ratio may refer to the doping ratio or the doping fraction.

For example, theoretically, a 100% doping ratio of Yb : Y₃Al₅O₁₂ is pure Yb₃Al₅O₁₂.
The doping fraction equals,

{\mathrm {\frac {N_{{\mathrm {atoms\ of\ dopant}}}}{N_{{\mathrm {atoms\ of\ solution\ which\ can\ be\ substituted\ with\ the\ dopant}}}}}}

References

↑ McGraw-Hill Dictionary of Chemistry. McGraw-Hill. p. 31. ISBN 0-07-141046-5.

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Atomic ratio

Atoms

Isotopes

Doping in laser physics

See also

References